Self interaction coefficient

A graphical integration of the Gibbs-Duhem equation is not necessary if an analytical expression for the partial properties of mixing is known. Let us assume that we have a dilute solution that can be described using the activity coefficient at infinite dilution and the self-interaction coefficients introduced in eq. (3.64). 

The relationship between the different self-interaction coefficients of component A and B, 7A and 7 , may in general be obtained in a similar way. 

Multiple linear regression analysis of Equation (1) can also be used and for this kxy is determined with as many different combinations of and statistical software packages or by a program based on the statistical equation in Appendix 1 (Section A 1.1.4.4). 

NMR Self-Diffusion of Desmopressin. The NMR-diffusion technique (3,10) offers a convenient way to measure the translational self-diffusion coefficient of molecules in solution and in isotropic liquid crystalline phases. The technique is nonperturbing, in that it does not require the addition of foreign probe molecules or the creation of a concentration-gradient in the sample it is direct in that it does not involve any model dependent assumptions. Obstruction by objects much smaller than the molecular root-mean-square displacement during A (approx 1 pm), lead to a reduced apparent diffusion coefficient in equation (1) (10). Thus, the NMR-diffusion technique offers a fruitful way to study molecular interactions in liquids (11) and the phase structure of liquid crystalline phases (11,12). 

Pulsed field gradient NMR (PFG-NMR) spectroscopy has been successfully used for probing interactions in several research fields.44-53 The method was developed by Stejskal and Tanner more than 40 years ago54 and allows the measurement of self-diffusion coefficient, D, which is defined as the diffusion coefficient in absence of chemical potential gradient. 

The last term is introduced within the self-consistent Hartree approximation (within the functional up to one vertex), //// = 10/9 accounts different coefficients in functional for the self-interaction terms (ri4 - for the given field d and dla)2 d )2 terms), cf [20], We presented da = 2k d t>ke lkfix, ... 

C4 hydrocarbons, presence of water in NaX, self-diffusion coefficients, 39 391-393 Chymotrypsin, 20 344, 356, 386, 387 Cl, see Configuration interaction Cirmarttaldehyde, hydrogenation of, 42 490... 

At low Q the experiments measure the collective diffusion coefficient D. of concentration fluctuations. Due to the repulsive interaction the effective diffusion increases 1/S(Q). Well beyond the interaction peak at high Q, where S(Q)=1, the measured diffusion tends to become equal to the self-diffusion D. A hydrodynamics factor H(Q) describes the additional effects on D ff=DaH(Q)/S Q) due to hydrodynamics interactions (see e.g. [342]). Variations of D(Q)S(Q) with Q (Fig. 6.28) may be attributed to the modulation with H(Q) displaying a peak, where S(Q) also has its maximum. For the transport in a crowded solution inside a cell the self-diffusion coefficient is the relevant parameter. It is strongly... 

To date, D coefficients of carbohydrates established with the PFGSE approactf - " have been undertaken to (1) validate the theoretical self-diffusion coefficients calculated from MD trajectories, (2) demonstrate the complexation of lanthanide cations by sugars,(3) probe the geometry of a molecular capsule formed by electrostatic interactions between oppositely charged P-cyclodextrins, (4) study the influence of concentration and temperature dependence on the hydrodynamic properties of disaccharides, and (5) discriminate between extended and folded conformations of nucleotide-sugars. ... 

Diffusion in a binary system may also be determined by measurement of the intradiffusion coefficient (sometimes referred to as the self-diffusion coefficient), D. In the case of intradiffusion, no net flux of the bulk diffusant occurs the molecules undergo an exchange process. Measurements are usually carried out by using trace amounts of labelled components in a system free of any gradients in the chemical potential. The molecular movement of the solute is governed by frictional interactions between labelled solute and solvent, and labelled solute and unlabelled solute. 

The value of the second virial coefficient A 2 can also be determined from the retention volume that is obtained from self-interaction chromatography (Aliamed et al., 2005 Winzor et al., 2007 Dumetz et al., 2008). The chromatographic retention factor k is calculated from the retention volume VT using the formula... 

Tessier, P.M., Lenhoff, A.M., Sandler, S.I. (2002). Rapid measurement of protein osmotic second virial coefficients by self-interaction chromatography. Biophysical Journal, 82, 1620-1631. 

Winzor, D.J., Scott, D.J., Wills, P.R. (2007). A simpler analysis for the measurement of second virial coefficients by self-interaction chromatography. Analytical Biochemistry, 371,21-25. 

Spiegler has used the friction model to describe a system consisting of sodium ions (1), chloride ions (2), water (3) and a charged matrix (4). He neglects the interaction of the sodium ions with the chloride ions. Then five independent measurements are needed to calculate the friction coefficients. Spiegler chose to be measured the self-diffusion coefficient... 

Self diffusion coefficients of deuterated toluene were measured, rather than protonated toluene in order to minimize the experimental difficulties associated with very long proton spin lattice relaxation times (T- ). Since the value of the T1 determines the length of time between pulse sequences, a long relaxation time leads to prohibitively long measurement times. Previous measurements (36-38) of proton and deuterium relaxation times in liquid toluene have been made as a function of temperature and pressure. The relaxation is due to dipolar interactions in protonated toluene and quadrupolar interactions in toluene-dg. Therefore, the relaxation times can be expected to increase with increasing temperature. However, the quadrupolar relaxed deuterium T. values are smaller than the proton T1... 

Also, a simple dependence like equation (1.72) can hardly be expected to hold for all chemical compounds without any exceptions under a variety of experimental conditions. The value of the self-diffusion coefficient of any component in the non-growing layer of a chemical compound is known to be strongly affected not only by the amount of vacancies but also by the mode of their formation and interaction with each other, the value of their charge, and other factors (see, for example, Refs 186-190). Perhaps, better results may in some cases be obtained using the equation... 

The aim of this Chapter is the development of an uniform model for predicting diffusion coefficients in gases and condensed phases, including plastic materials. The starting point is a macroscopic system of identical particles (molecules or atoms) in the critical state. At and above the critical temperature, Tc, the system has a single phase which is, by definition, a gas or supercritical fluid. The critical temperature is a measure of the intensity of interactions between the particles of the system and consequently is a function of the mass and structure of a particle. The derivation of equations for self-diffusion coefficients begins with the gaseous state at pressures p below the critical pressure pc. A reference state of a hypothetical gas will be defined, for which the unit value D = 1 m2/s is obtained at p = 1 Pa and a reference temperature, Tr. Only two specific parameters, Tc, and the critical molar volume, VL, of the mono-... 

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